Raman investigation of MoSe2 was carried out with eight different excitation energies. Seven peaks, including E1g, A1g, E2g(1), and A2u(2) peaks are observed in the range of 100-400 cm(-1). The phonon modes are assigned by comparing the peak positions with theoretical calculations. The intensities of the peaks are enhanced at different excitation energies through resonance with different optical transitions. The A1g mode is enhanced at 1.58 and 3.82 eV, which are near the A exciton energy and the band-to-band transition between higher energy bands, respectively. The E2g(1) mode is strongly enhanced with respect to the A1g mode for the 2.71- and 2.81-eV excitations, which are close to the C exciton energy. The different enhancements of the A1g and E2g(1) modes are explained in terms of the symmetries of the exciton states and the exciton-phonon coupling. Other smaller peaks including E1g and A2u(2) are forbidden but appear due to the resonance effect near optical transition energies.